Partition Statistics for Cubic Partition Pairs
نویسندگان
چکیده
منابع مشابه
Partition Statistics for Cubic Partition Pairs
In this brief note, we give two partition statistics which explain the following partition congruences: b(5n + 4) ≡ 0 (mod 5), b(7n + a) ≡ 0 (mod 7), if a = 2, 3, 4, or 6. Here, b(n) is the number of 4-color partitions of n with colors r, y, o, and b subject to the restriction that the colors o and b appear only in even parts.
متن کاملIdentically Distributed Pairs of Partition Statistics
We show that many theorems which assert that two kinds of partitions of the same integer n are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics X and Y that have identical distribution functions. The method is an extension of the principle of sieve-equivalence, and it yields simple criteria under which we can...
متن کاملSet partition patterns and statistics
A set partition σ of [n] = {1, . . . , n} contains another set partition π if restricting σ to some S ⊆ [n] and then standardizing the result gives π. Otherwise we say σ avoids π. For all sets of patterns consisting of partitions of [3], the sizes of the avoidance classes were determined by Sagan and by Goyt. Set partitions are in bijection with restricted growth functions (RGFs) for which Wach...
متن کاملADMISSIBLE PARTITION FOR BL-GENERAL FUZZY AUTOMATON
In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...
متن کاملA partition-based algorithm for clustering large-scale software systems
Clustering techniques are used to extract the structure of software for understanding, maintaining, and refactoring. In the literature, most of the proposed approaches for software clustering are divided into hierarchical algorithms and search-based techniques. In the former, clustering is a process of merging (splitting) similar (non-similar) clusters. These techniques suffered from the drawba...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/615